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<div class="title">matrix.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#ifndef _MATRIX_H</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#define _MATRIX_H</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#include &lt;boost/numeric/ublas/matrix.hpp&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="preprocessor">#include &lt;boost/numeric/ublas/io.hpp&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#include &lt;boost/numeric/ublas/lu.hpp&gt;</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="preprocessor">#include &lt;cassert&gt;</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;</div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="keyword">namespace </span>bnu = boost::numeric::ublas;</div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;</div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;T get_determinant(bnu::matrix&lt;T&gt;&amp; matrix)</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;{</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;    assert(matrix.size1() == matrix.size2());</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;    bnu::permutation_matrix&lt;T&gt; perm_matrix(matrix.size1());</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;    T determinant = 1.0;</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;    <span class="keywordflow">if</span>(bnu::lu_factorize(matrix, perm_matrix))</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;    {</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;        <span class="keywordflow">return</span> 0.0;</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    }</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    {</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;        <span class="keywordflow">for</span>(std::size_t idx = 0; idx &lt; matrix.size1(); idx++)</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;        {</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;            <span class="comment">//multiply all the elements on the diagonal</span></div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;            <span class="comment">//and change sign for every transposition</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;            determinant *= matrix(idx, idx);</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;            <span class="keywordflow">if</span>(idx != perm_matrix(idx))</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;                determinant *= -1.0;</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;        }</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    }</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    <span class="keywordflow">return</span> determinant;</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;};</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;<span class="keywordtype">bool</span> get_inverse(bnu::matrix&lt;T&gt;&amp; matrix, bnu::matrix&lt;T&gt;&amp; inverse)</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;{</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    assert(matrix.size1() == matrix.size2());</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;    bnu::permutation_matrix&lt;T&gt; perm_matrix(matrix.size1());</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    <span class="keywordflow">if</span>(bnu::lu_factorize(matrix, perm_matrix))</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;    {</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    }</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    inverse.resize(matrix.size1(), matrix.size1());</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    inverse.assign(bnu::identity_matrix&lt;T&gt;(matrix.size1()));</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    <span class="comment">//solve AX=I</span></div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    bnu::lu_substitute(matrix, perm_matrix, inverse);</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;};</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;<span class="keywordtype">void</span> rref(bnu::matrix&lt;T&gt;&amp; matrix)</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;{</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    std::size_t pivot_col = 0;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="keywordflow">for</span>(std::size_t rows_idx = 0; rows_idx &lt; matrix.size1(); rows_idx++)</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    {</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;        <span class="keywordflow">if</span>(pivot_col &gt;= matrix.size2())</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;            <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;        <span class="comment">//search for a pivot if needed</span></div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;        std::size_t rows1_idx = rows_idx;</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;        <span class="keywordflow">while</span>(matrix(rows1_idx, pivot_col) == 0.0)</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        {</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;            rows1_idx++;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;            <span class="keywordflow">if</span>(rows1_idx &gt;= matrix.size1())</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;            {</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;                rows1_idx = rows_idx;</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;                pivot_col++;</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;                <span class="keywordflow">if</span>(pivot_col &gt;= matrix.size2())</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;                    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;            }</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;        }</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;        <span class="comment">//swap rows if necessary</span></div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;        <span class="keywordflow">if</span>(rows_idx != rows1_idx)</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;        {</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;            bnu::vector&lt;T&gt; temp = bnu::row(matrix, rows_idx);</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;            bnu::row(matrix, rows_idx) = bnu::row(matrix, rows1_idx);</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;            bnu::row(matrix, rows1_idx) = temp;</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;        }</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;        <span class="comment">//divide the row by the pivot</span></div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;        T pivot = matrix(rows_idx, pivot_col);</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;        <span class="keywordflow">for</span>(std::size_t cols_idx = 0; cols_idx &lt; matrix.size2(); cols_idx++)</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;        {</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;            assert(pivot != 0.0);</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;            <span class="keywordflow">if</span>(pivot != 1.0)</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;                matrix(rows_idx, cols_idx) /= pivot;</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;        }</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;        <span class="comment">//elimination</span></div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;        <span class="keywordflow">for</span>(std::size_t rows2_idx = 0; rows2_idx &lt; matrix.size1(); rows2_idx++)</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;        {</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;            <span class="keywordflow">if</span>(rows2_idx != rows_idx)</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;            {</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;                T piv_elim = matrix(rows2_idx, pivot_col);</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;                <span class="keywordflow">for</span>(std::size_t cols_idx = 0; cols_idx &lt; matrix.size2(); cols_idx++)</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;                {</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;                    matrix(rows2_idx, cols_idx) -= piv_elim * matrix(rows_idx, cols_idx);</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;                }</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;            }</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;        }</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;        <span class="comment">//std::cout&lt;&lt;matrix&lt;&lt;&quot;\n&quot;;</span></div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;        pivot_col++;</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    }</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;};</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;<span class="preprocessor"></span></div>
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